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How many solutions does this equation have?\newline56(x−3)+13x=12x+23x−5\frac{5}{6}(x - 3) + \frac{1}{3}x = \frac{1}{2}x + \frac{2}{3}x - 5\newlineChoices:\newline(A) none\newline(B) one\newline(C) two\newline(D) infinitely many

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Find the number of solutions to a linear equationright chevron icon

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Q. How many solutions does this equation have?\newline56(x−3)+13x=12x+23x−5\frac{5}{6}(x - 3) + \frac{1}{3}x = \frac{1}{2}x + \frac{2}{3}x - 5\newlineChoices:\newline(A) none\newline(B) one\newline(C) two\newline(D) infinitely many
  1. Combine and Simplify Left Side: Simplify the left side of the equation by combining terms. \newline56(x−3)+13x\frac{5}{6}(x - 3) + \frac{1}{3}x \newline= 56x−52+13x\frac{5}{6}x - \frac{5}{2} + \frac{1}{3}x \newline= (106x+26x)−52(\frac{10}{6}x + \frac{2}{6}x) - \frac{5}{2} \newline= 126x−52\frac{12}{6}x - \frac{5}{2} \newline= 2x−522x - \frac{5}{2}
  2. Combine and Simplify Right Side: Simplify the right side of the equation by combining terms.\newline12x+23x−5\frac{1}{2}x + \frac{2}{3}x - 5\newline= (36x+46x)−5\left(\frac{3}{6}x + \frac{4}{6}x\right) - 5\newline= 76x−5\frac{7}{6}x - 5
  3. Set Equal and Solve for x: Set the simplified left side equal to the simplified right side and solve for xx.
    2x−52=76x−52x - \frac{5}{2} = \frac{7}{6}x - 5
    Multiply all terms by 66 to clear the fractions:
    12x−15=7x−3012x - 15 = 7x - 30
    Subtract 7x7x from both sides:
    5x−15=−305x - 15 = -30
    Add 1515 to both sides:
    5x=−155x = -15
    Divide by 55:
    x=−3x = -3

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